Continuous-Time Robust Control for Cancer Treatment Robots

TL;DR

The paper addresses safe real-time control for cancer-treatment robots under model uncertainties, including nonlinear dynamics in m-link serial manipulators. It proposes a continuous-time robust-control framework that uses polytopic differential inclusions to represent the nonlinear plant and a structured uncertainty block for mu-synthesis, resulting in a single-layer controller. Demonstrations on a 2R robot show that a fixed-structure, multi-block controller can achieve robust stability with $\mu$-LLFT$(P,K) < 1$ (e.g., $0.9998$–$0.9999$) while dramatically reducing controller order from high-order designs (e.g., 132) to about 3 per block. This work highlights the practicality of robust, real-time cancer-treatment robotics and points to future extensions to parallel robots and full system integration.

Abstract

The control system in surgical robots must ensure patient safety and real time control. As such, all the uncertainties which could appear should be considered into an extended model of the plant. After such an uncertain plant is formed, an adequate controller which ensures a minimum set of performances for each situation should be computed. As such, the continuous-time robust control paradigm is suitable for such scenarios. However, the problem is generally solved only for linear and time invariant plants. The main focus of the current paper is to include m-link serial surgical robots into Robust Control Framework by considering all nonlinearities as uncertainties. Moreover, the paper studies an incipient problem of numerical implementation of such control structures.

Figures (5)

• Figure 1: General m-link cancer treatment serial robot.
• Figure 2: The generalized plant $P$ and its interconnections with the uncertainty block $\bm{\Delta}$ and the controller $K$.
• Figure 3: Magnitude Bode diagram of the linear polytopic differential inclusion $G_{\Delta}(s)$.
• Figure 4: The evolution of the sensitivity and the complementary sensitivity functions for both nominal model and $20$ Monte Carlo simulations, along with the imposed shapes via the augmentation process (red line).
• Figure 5: Bode magnitude representations of the robust high-order controller (blue) and of the fixed-structure robust controller (orange).